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A300321 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 16, 16, 16, 8, 13, 50, 61, 61, 50, 13, 21, 112, 186, 735, 186, 112, 21, 34, 348, 977, 3486, 3486, 977, 348, 34, 55, 1028, 3875, 25797, 31345, 25797, 3875, 1028, 55, 89, 2796, 15976, 203113, 345605, 345605, 203113, 15976, 2796, 89 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

..1....2.....3........5.........8..........13............21...............34

..2....4.....4.......16........50.........112...........348.............1028

..3....4....16.......61.......186.........977..........3875............15976

..5...16....61......735......3486.......25797........203113..........1378779

..8...50...186.....3486.....31345......345605.......4705725.........55447293

.13..112...977....25797....345605.....8002885.....178277369.......3616312721

.21..348..3875...203113...4705725...178277369....7221094975.....257924884697

.34.1028.15976..1378779..55447293..3616312721..257924884697...16292595627604

.55.2796.69695.10140973.678378012.80381600442.9967764866344.1108503299923830

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 40] for n>43

EXAMPLE

Some solutions for n=5 k=4

..0..1..0..0. .0..1..0..0. .0..0..0..0. .0..1..1..0. .0..0..1..1

..1..0..0..0. .1..0..0..0. .1..1..0..0. .1..1..1..1. .0..0..0..0

..1..1..0..0. .1..1..0..0. .1..1..1..1. .1..1..1..1. .0..0..1..1

..1..1..1..0. .1..1..1..1. .1..1..0..0. .1..1..1..1. .1..0..1..1

..1..1..1..0. .0..1..0..0. .0..0..0..0. .0..0..1..0. .1..0..1..1

CROSSREFS

Column 1 is A000045(n+1).

Column 2 is A298148.

Sequence in context: A299052 A299814 A299689 * A026254 A091525 A091524

Adjacent sequences:  A300318 A300319 A300320 * A300322 A300323 A300324

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 02 2018

STATUS

approved

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Last modified October 21 18:51 EDT 2021. Contains 348155 sequences. (Running on oeis4.)